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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': -4, 'A5': 0, 'A6': 0, 'A7': 10, 'A8': 0, 'A9': 0, 'Lhash': '596746178291646844,596746178291646844', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [-2.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [3.7796447300922726, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 75.61535118861151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '1185921.1', 'coefficient_field': '1.1.1.1', 'conductor': 1185921, 'conductor_radical': 33, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1], [1, 0, 10, 0, 25], [1, -10, 39, -70, 49], [1], [1, -4, 30, -52, 169], [1, 0, 34, 0, 289], [1, 14, 87, 266, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, -22, 183, -682, 961], [1, -22, 195, -814, 1369], [1, 0, 82, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, 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'positive_zeros': ['1.04628882090551819052986550472340', '1.04628882090551819052986550472340', '2.33436956052754417074709546789325', '2.33436956052754417074709546789325', '4.10163309596027718433915629505997', '4.10163309596027718433915629505997', '4.46927736296465408535190629372636', '4.46927736296465408535190629372636', '5.44366242309248335244474381902091', '5.44366242309248335244474381902091', '6.34989393601049354736426581843581', '6.34989393601049354736426581843581', '7.85350411050304424040374786608053', '7.85350411050304424040374786608053', '8.157799715862211353426737114370343', '8.157799715862211353426737114370343', '8.865764499575516828484003461556969', '8.865764499575516828484003461556969', '9.835215950476228006589046857848727', '9.835215950476228006589046857848727', '10.73523734786457418306615049108900', '10.73523734786457418306615049108900', '11.33972098221797814076111794654997', '11.33972098221797814076111794654997', '12.17256485280654734778650090930600', '12.17256485280654734778650090930600', '13.04831728926521935406591876709309', '13.04831728926521935406591876709309', '13.79340234850264329551997003646644', '13.79340234850264329551997003646644'], 'prelabel': '4-33e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.948848721131255, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'U(1)', 'symmetry_type': 'symplectic', 'trace_hash': 1193492356583293688, 'z1': {'__RealLiteral__': 0, 'data': '1.04628882090551819052986550472340', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.04628882090551819052986550472340', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.33436956052754417074709546789325', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 75.61535118861151, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 1185921, 'conductor_radical': 33, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, 10, 0, 0, 0, 0, 0, 4, 0, 0, 12, 0, 0, -14, 0, 0, 0, 0, 0, -10, 0, 0, -40, 0, 0, 22, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 61, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -32, 0, 0, 22, 0, 0, 0, 0, 0, 34, 0, 0, 56, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 10, 0, 0, 40], 'euler11': [1, 0, 0, 0, 0], 'euler13': [1, -4, 30, -52, 169], 'euler17': [1, 0, 34, 0, 289], 'euler19': [1, 14, 87, 266, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, 0, 46, 0, 529], 'euler29': [1, 0, 58, 0, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -22, 183, -682, 961], 'euler37': [1, -22, 195, -814, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, -16, 150, -688, 1849], 'euler47': [1, 0, 94, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, 118, 0, 3481], 'euler61': [1, 2, 123, 122, 3721], 'euler67': [1, -22, 255, -1474, 4489], 'euler7': [1, -10, 39, -70, 49], 'euler71': [1, 0, 142, 0, 5041], 'euler73': [1, -34, 435, -2482, 5329], 'euler79': [1, 26, 327, 2054, 6241], 'euler83': [1, 0, 166, 0, 6889], 'euler89': [1, 0, 178, 0, 7921], 'euler97': [1, -10, 219, -970, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 0, 0, 0, 0], [1, 0, 10, 0, 25], [1, -10, 39, -70, 49], [1, 0, 0, 0, 0], [1, -4, 30, -52, 169], [1, 0, 34, 0, 289], [1, 14, 87, 266, 361], [1, 0, 46, 0, 529], [1, 0, 58, 0, 841], [1, -22, 183, -682, 961], [1, -22, 195, -814, 1369], [1, 0, 82, 0, 1681], [1, -16, 150, -688, 1849], [1, 0, 94, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, 118, 0, 3481], [1, 2, 123, 122, 3721], [1, -22, 255, -1474, 4489], [1, 0, 142, 0, 5041], [1, -34, 435, -2482, 5329], [1, 26, 327, 2054, 6241], [1, 0, 166, 0, 6889], [1, 0, 178, 0, 7921], [1, -10, 219, -970, 9409]], 'index': 16, 'instance_types': ['ECNF'], 'instance_urls': ['EllipticCurve/2.0.3.1/131769.1/CMa'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-33e4-1.1-c1e2-0-16', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-33e4-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.948848721131255, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1193492356583293688, 'z1': {'__RealLiteral__': 0, 'data': '1.04628882090551819052986550472340', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '596746178291646844,596746178291646844', 'Lhash_array': ['596746178291646844', '596746178291646844'], 'label': '4-33e4-1.1-c1e2-0-16', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/131769.1/CMa'}